Multiplicityof solution for a singular problem involving the $ \varphi $-Hilfer derivative and variable exponents

Wafa M. Shammakh; Raghad D. Alqarni; Hadeel Z. Alzumi; Abdeljabbar Ghanmi; Wafa M. Shammakh; Raghad D. Alqarni; Hadeel Z. Alzumi; Abdeljabbar Ghanmi

doi:10.3934/math.2025209

AIMS Mathematics

2025, Volume 10, Issue 3: 4524-4539. doi: 10.3934/math.2025209

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Multiplicityof solution for a singular problem involving the $ \varphi $-Hilfer derivative and variable exponents

Department of Mathematics and Statistics, Faculty of Sciences, University of Jeddah, Jeddah, Saudi Arabia

Received: 30 December 2024 Revised: 03 February 2025 Accepted: 24 February 2025 Published: 03 March 2025
MSC : 31B30, 35J35, 35J60

This paper dealt with the existence of multiple solutions for some singular $ p(s) $-Laplacian problems involving the $ \varphi $-Hilfer derivative. Precisely, we combined the variational method with the Nehari manifold to prove that such a problem admited two nontrivial solutions. An example was presented to illustrate the effectiveness of our main result.
- variational methods,
- Nehari manifold,
- Sobolev space with variable exponents,
- $ \varphi $-Hilfer derivative
Citation: Wafa M. Shammakh, Raghad D. Alqarni, Hadeel Z. Alzumi, Abdeljabbar Ghanmi. Multiplicityof solution for a singular problem involving the $ \varphi $-Hilfer derivative and variable exponents[J]. AIMS Mathematics, 2025, 10(3): 4524-4539. doi: 10.3934/math.2025209

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Abstract

This paper dealt with the existence of multiple solutions for some singular $ p(s) $-Laplacian problems involving the $ \varphi $-Hilfer derivative. Precisely, we combined the variational method with the Nehari manifold to prove that such a problem admited two nontrivial solutions. An example was presented to illustrate the effectiveness of our main result.

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